The Pope commonly refers to the Bishop of Rome, the leader of the Catholic Church and head of state of Vatican City. There hasn't been a legitimate Pope since Pope Pius XII died in 1958, a situation known as sede vacante (due to the seat of St. Peter being vacant). The modernist imposters who presently control the Vatican are Anti-Popes, leaders of the Vatican II Church, a new religion which believes in the Second Vatican Council, a heretical robber council. Jorge Mario Bergoglio, the present leader of this counter-church cannot be a Pope because he holds views deemed heretical to the Catholic faith and only a Catholic can be Pope.
The term Pope ultimately originates from the Greek word papas, meaning father (the Latin word is papa). During the early days of the Christian Church, the word was used in Anatolia to denote a bishop. The Church of Alexandria in Egypt, one of the five ancient patriarchates of the Christian Church, adopted the title "Pope of Alexandria" around the time of 250, during the reign of St. Dionysius the Great (today the Coptic Church continues to use this title, while the Orthodox leader calls himself "Patriarch of Alexandria"). In the West, the term Pope was used in reference to the Bishop of Rome from the time of St. Leo the Great in the 5th century. This began to be used clearly and emphatically in reference to the Bishop of Rome, with the implications of holding universal jurisdiction over all bishops, during the reign of St. Pope Gregory VII in 1073.
The office of the pope is called the Papacy; his ecclesiastical jurisdiction is called the "Holy See" (Sancta Sedes in Latin) or "Apostolic See" (the latter on the basis that both St. Peter and St. Paul were martyred at Rome).
In addition to his spiritual role, the pope is Head of State of the independent sovereign state of the Vatican City, a city-state entirely enclaved by the city of Rome. Before 1870, the pope's temporal authority extended over a large area of central Italy: the territory of the Papal States. The papacy retained sovereign authority over the Papal States until the Italian unification of 1870; a final political settlement with the Italian government was not reached until the Lateran Treaty of 1929.
For over a thousand years, popes played powerful roles in Western Europe, often struggling with monarchs for power over wide-ranging affairs of church and state, crowning emperors (Charlemagne was the first emperor crowned by a pope) and regulating disputes among secular rulers. The Bishop of Rome continued to be nominally allied with and part of the civil structure of the (Byzantine) Roman Empire until the 8th century, when the Donation of Pepin gave Rome and the surrounding area to the full sovereignty of the pope, over which the popes already had been de facto rulers, creating the Papal States that lasted until 1870. For centuries, the forged Donation of Constantine also provided the basis for the papacy's claim of political supremacy over the entire former Western Roman Empire.
Gradually forced to give up secular power, popes have come to focus again almost exclusively on spiritual matters. Over the centuries, popes' claims of spiritual authority have been ever more clearly expressed since the first centuries, culminating in the proclamation of the dogma of papal infallibility for those rare occasions the pope speaks ex cathedra (literally "from the chair (of Peter)") when issuing a solemn definition of faith or morals. The last such occasion was in the year 1950 with the definition of the dogma of the Assumption of Mary.